Cremona's table of elliptic curves

2730 = 2 · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	2730a	Isogeny class
Conductor	2730	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	9931302391046400 = 28 · 38 · 52 · 72 · 136	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -4 13+  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-85438,-8366732]	[a1,a2,a3,a4,a6]
Generators	[-197:1030:1]	Generators of the group modulo torsion
j	68973914606086620649/9931302391046400	j-invariant
L	1.8306492028308	L(r)(E,1)/r!
Ω	0.28192668666427	Real period
R	3.2466759789414	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21840bw2 87360db2 8190bn2 13650cv2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730a2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	+	+	+	-4	+	6	0	4	-2	4	2	-2	8	-8	-2	-8	6	-12	0	6	-8	-4	-10	14

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Quadratic twists for elliptic curve 2730a2

-4	8	-3	5	-7	13
21840bw2	87360db2	8190bn2	13650cv2	19110bl2	35490cs2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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